22nd December 2008

If x1,...,xn ε R and y1,...,yn ε R are the components of x and y ;

samajh me nahi aaya :( " components"

mera dimag aaj anhi chal raha lagta hai :(

:)

Now its alright

Cheers to me.. :)

Clearly equlity holds when all x_is or all y_is are zero

{x₁²+x₂²+...................+x_n²}{y₁²+y₂²+.............+y_n²} - {x₁y₁+.......................x_ny_n}²

=1/2 Σ{x_p²y_q²+x_q²y_p²-2x_py_px_qy_q} note that inside Σ p≠q and p,q=1,2,3,4,.......................n

the equality sign holds iff x_py_q-x_qy_p=0 i.e. iff x_p:x_q::y_p:y_q , for every pair of suffixes p,q i.e.e iff x₁:x₂:.............:x_n::y₁:y₂:...............y_n

this is the first of the proofs i have